A Note on the Generalized Petersen Graphs That Are Also Cayley Graphs

The aim of this note is to present a short proof of a result of Nedela and Škoviera (J. Graph Theory19(1995, 1–11)) concerning those generalized Petersen graphs that are also Cayley graphs. In that paper the authors chose the heavy weaponry of regular maps on closed connected orientable surfaces. Our proof relies on the general characterization of Cayley graphs and on the complete determination of the automorphism groups of the generalized Petersen graphs. With both of them in hand, it is easy to find the intersection of the two graph families.